theorem Th41:
  not x == 0_No & x * y == 1_No implies y == x"
proof
  assume
A1:not x == 0_No & x * y == 1_No;
  then
A2: x * x" == 1_No by Th33;
  (x"* x) * y == x"* (x * y) == 1_No * x" by A1,SURREALR:54,SURREALR:69;
  then 1_No * y == (x"* x) * y == x" by A2,SURREALR:54,SURREALO:4;
  hence thesis by SURREALO:4;
end;
